Question: Solve for $x$ and $y$ using elimination. ${x+5y = 47}$ ${2x+3y = 31}$
Explanation: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Multiply the top equation by $-2$ ${-2x-10y = -94}$ $2x+3y = 31$ Add the top and bottom equations together. $-7y = -63$ $\dfrac{-7y}{{-7}} = \dfrac{-63}{{-7}}$ ${y = 9}$ Now that you know ${y = 9}$ , plug it back into $\thinspace {x+5y = 47}\thinspace$ to find $x$ ${x + 5}{(9)}{= 47}$ $x+45 = 47$ $x+45{-45} = 47{-45}$ ${x = 2}$ You can also plug ${y = 9}$ into $\thinspace {2x+3y = 31}\thinspace$ and get the same answer for $x$ : ${2x + 3}{(9)}{= 31}$ ${x = 2}$